How do you simplify 14:7:21

Answer:

20 movies ; $70

Step-by-step explanation:

Company 1:

Monthly charge = $40 ; additional = 1.5 per movie

Let number of movies = x ; t = cost

Equation 1:

y = 40 + 1.5x

Company 2:

Monthly charge = $30

Additional = $2 per movie

Equation 2:

y = 30 + 2x

1) for equation 1 = equation 2

40 + 1.5x = 30 + 2x

40 - 30 = 2x - 1.5x

10 = 0.5x

x = 10/0.5

x = 20

Hence, 20 movies

B.)

y = 30 + 2x

y = 30 + 2(20)

y = 30 + 40

y = $70

Euler's theorem, also known as Euler's formula, is a fundamental result in mathematics that relates the exponential function, complex numbers, and trigonometry.

The theorem states that for any real number x, the complex exponential function \(e^ix\) can be expressed as the sum of a cosine function cos(x) and a sine function sin(x), where i is the imaginary unit. In other words, \(e^ix\) = cos(x) + i sin(x). This result has important applications in many fields, including physics, engineering, and computer science, and is used to analyze periodic phenomena such as sound waves and electromagnetic radiation.

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Answer:

25% would be the answer hope this helps. have a good day!

Answer: 75%

Step-by-step explanation:

0.75 x 20 = 15

Explanation:

We have three numbers that aren't even, and they are {1,3,5}

There are three numbers that are even, and they are {2,4,6}

The odds in favor of not getting an even number is 3:3 = 1:1

To list the odds in favor, you write the number of ways to get what you want, followed by a colon, then the number of ways to get what you don't want. In this case, both counts are 3. The ratio 3:3 reduces to 1:1 after dividing both parts by 3.

Answer:

1:1

Step-by-step explanation:

how many odd sections are even: 3

how many sections are not even: 3

the odds are 3 : 3= 1:1

odds are what you expect to come out versus what you don't expect(favorable to un favorable).

confusion comes in when talking about probability

probability is what you want to come out versus the total chances whether odd or even(favorable to total outcomes). eg

in this example

the probability of it not landing on the even number is:

number of odd sections=         3     =   1:2

number of total outcomes=     6

The value of [f(a+h)−f(a)]/h is equal to 4h + 2. This means that as the value of h changes, the expression will evaluate to 4 times the value of h plus 2. It represents the rate of change of the function \(f(x) = 3 + 2x^2\) at a particular point a.

To calculate this value, we need to substitute the given function \(f(x) = 3 + 2x^2\) into the expression [f(a+h)−f(a)]/h and simplify it.

First, let's find f(a+h):

\(f(a+h) = 3 + 2(a+h)^2\\= 3 + 2(a^2 + 2ah + h^2)\\= 3 + 2a^2 + 4ah + 2h^2\)

Next, let's find f(a):

\(f(a) = 3 + 2a^2\)

Now, substitute these values into the expression [f(a+h)−f(a)]/h:

\([f(a+h)-f(a)]/h = [(3 + 2a^2 + 4ah + 2h^2) - (3 + 2a^2)]/h\\= (4ah + 2h^2)/h\\= 4a + 2h\)

Therefore, [f(a+h)−f(a)]/h simplifies to 4a + 2h, which is equal to 4h + 2.

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TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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Answer:

30 feet

Step-by-step explanation:

i used a ruler, mm side. 1 mm = 1 foot

draw a horizontal line.

draw a vertical line 28mm high

use a protractor to find a line that connects to the base and top of vertical line.

measure said line

Answer:

Step-by-step explanation:

\text{sin }\color{purple}{71}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{28}}{\color{#EB0000}{x}}

sin 71=

hypotenuse

opposite

​

=

x

28

​

\text{sin }71=

sin 71=

\,\,\frac{28}{x}

x

28

​

\frac{\text{sin }71}{1}=

1

sin 71

​

=

\,\,\frac{28}{x}

x

28

​

x\text{ sin }71=

x sin 71=

\,\,28

28

Cross multiply.

\frac{x\text{ sin }71}{\text{ sin }71}=

sin 71

x sin 71

​

=

\,\,\frac{28}{\text{ sin }71}

sin 71

28

​

Divide both sides by sin 71

x=\frac{28}{\text{ sin }71}=29.613379...\approx29.61

x=

sin 71

28

​

=29.613379...≈29.61

Answer:

-3

Step-by-step explanation:

11-8=3 8-8=0 0-3=-3

yes, for your x to be positive and to make it remain on the left hand side you actually have to add 4x to both side to eliminate x from the right hand side.

The least common denominator of the given rational expressions is 2x^3(x + 4). This is the smallest expression that both denominators can be multiplied by to obtain equivalent fractions with a common denominator.

To find the least common denominator (LCD) of the rational expressions 1/(2x^2 + 8x)and 10/x^2, we need to determine the common factors in the denominators and then multiply them.

The first denominator, 2x^2 + 8x, can be factored as 2x(x + 4), where x + 4 is a linear factor.

The second denominator,\(x^2\), is already in its factored form.

To find the LCD, we need to consider all the factors and their highest powers. In this case, we have:

2x(x + 4) and \(x^2\)

Since the highest power of x in 2x(x + 4) is 1 and in \(x^2\) is 2, the LCD must include both factors with their highest powers. Therefore, the LCD is:

LCD = 2x(x + 4)(x^2)

Simplifying further, we can write the LCD as:

LCD = 2x^3(x + 4)

So, the least common denominator of the given rational expressions is 2x^3(x + 4). This is the smallest expression that both denominators can be multiplied by to obtain equivalent fractions with a common denominator.

Using the LCD, we can then add or subtract the rational expressions by multiplying each term by the necessary factors to achieve the common denominator.

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we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)

and tan(A-B)= (tanA-tanB)/(1+tanAtanB)

tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)

tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)

now add the equation (1) and (2) which is LHS of question. So we get:

{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS

Hence proved.

Answer:

x<-4

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

Put the numbers where the variables are and do the arithmetic.

  13 -0.75w +8x

  = 13 -0.75(12) +8(1/2) . . . . . substitute for w and x

  = 13 -9 +4

  = 4 +4

  = 8

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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Answer: 15

Step-by-step explanation:

So it is pretty much 60/4 which is easy 15 here is the work

1 5

4 6 0

- 4

2 0

- 2 0

0

Answer:

x ≥ $15

Step-by-step explanation:

At least means ≥

4x ≥ $60     Replace the inequality sign with an = sign and solve the equation.

4x = $60

x  = $60 ÷ 4

x = $15                 Now put the inequality sign back into the problem

 x ≥ $15

After calculating we get, x-intercept is (-8/3, 0), y-intercept is (0, -16), slope is -6, f(3) = (-34) and So when f(x) = 110, x = -21.

To find the characteristics of the linear function 30x + 5y = -80:

To find the x-intercept, we set y = 0 and solve for x:

30x + 5(0) = -80

30x = -80x = -8/3

So the x-intercept is (-8/3, 0).

To find the y-intercept, we set x = 0 and solve for y:

30(0) + 5y = -80

5y = -80y = -16

So the y-intercept is (0, -16).

To find the slope, we solve for y in terms of x by rearranging the equation to slope-intercept form, y = mx + b:

30x + 5y = -80

5y = -30x - 80y = -6x - 16

So the slope is -6.

To find f(3), we substitute x = 3 into the equation and solve for y:

30(3) + 5y = -80

90 + 5y = -80

5y = -170y = -34

So f(3) = (-34).

To find x when f(x) = 110, we substitute y = 110 into the equation and solve for x:

30x + 5(110) = -80

30x + 550 = -80

30x = -6

30x = -21

So when f(x) = 110, x = -21.

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Answer: $25.85 assuming annual compounding.

Step-by-step explanation:

PV=470

I/Y=5.5

N=1

CPT_FV

Answer:

Scuba-4-All's initial cost is $55

Scuba palace's initial cost is $30

Step-by-step explanation:

Initial cost is the cost when at zero hours or 0 x value

Answer:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

\(\dfrac{\partial M}{\partial y}= 6x+2y+6\)

and

N = 6x +2y

\(\dfrac{\partial N}{\partial x}= 6\)

∴

\(f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y)\)

f(x) = 1

Now, the integrating factor can be computed as:

\(\implies e^{\int fxdx}\)

\(\implies e^{\int (1)dx}\)

the integrating factor = \(e^x\)

From the given equation:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

Let us multiply the above given equation by the integrating factor:

i.e.

\((6xy+y^2 +6y)dx +(6x +2y)dy=0\)

\((6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0\)

\(6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0\)

By rearrangement:

\(6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0\)

Let assume that:

\(6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)\)

and:

\(y^2e^xdx +e^x2ydy=d(y^2e^x)\)

Then:

\(d(6xe^xy)+d(y^2e^x) = 0\)

\(6d (xe^xy) + d(y^2e^x) = 0\)

By integration:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

Therefore, mean of the chi-square distribution has now become 0 and is not a characteristic of the chi square distribution, hence this is how the given chi square problem is resolved.

To compare actual outcomes with predictions, statistical tests like the chi-square test are performed. This test's goal is to establish whether a discrepancy between observed and expected data results from chance or a connection between the variables under study.

Here,

The characteristics of the a chi square test must be discovered.

1. Untrue

A chi square distribution's mean is the same as its degree of freedom.

B) True

Asymmetry exists in the chi-square distribution.

C) True

Both 0 and 1 are valid values for the chi square.

Its foundation is a sum of the squared differences, hence it will never be negative.

D) True

For every degree of freedom, there is a separate chi-square distribution.

The freedom level is n - 1 when working with a singular population variance.

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Answer:

  1/20 g/mL

Step-by-step explanation:

You want the fraction form of the ratio in grams per mL of 50 g in 1000 mL.

The word "per" in this context means "divided by." That is, "grams per mL" means "grams divided by milliliters." That ratio looks like ...

  \(\dfrac{50\text{ g}}{1000\text{ mL}}=\boxed{\dfrac{1}{20}\text{ g/mL}}\)

Answer:

\( \displaystyle \large{x(7 {x}^{2} + 4)}\)

Step-by-step explanation:

We are given the cubic expression:

\( \displaystyle \large{7 {x}^{3} + 4x}\)

In the expression, there exists same x-term but not like term.

Factor using LCF (Least Common Factor which is x)

\( \displaystyle \large{x(7 {x}^{2} + 4)}\)

From 7x^2+4, the expression is not factorable and thus:-

\( \displaystyle \large{x(7 {x}^{2} + 4)}\)

is the simplified form.

The correct option which would decrease the margin of error is Option B.

The margin of error is inversely proportional to the square root of the sample size. This means that increasing the sample size will decrease the margin of error.

Constructing a 90% confidence interval will increase the margin of error, and constructing a 95% confidence interval will increase the margin of error even more. This is because a higher confidence level requires a wider confidence interval.

Therefore, the correct option is using a sample size of 200.

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Answer:

Write an equation of the parabola in vertex form

1. Passes through (-5,0) and has vertex (-2,1)

2. Passes through (4,10) and has vertex (0,0)

3. Passes through (6,-1) and has vertex (14,-20)

4. Passes through (-5,-3) and has vertex (7,12)

5. Passes through (9,15) and has vertex (-6,21)

6. Passes through (0,0) and has vertex (-10,-43jkdiow

There are several different measures of central tendency that can be used to describe the average of a data set. The three most common measures of central tendency are the mean, median, and mode. Each of these measures can be used to describe different types of data. Here are three examples of different types of data and the measures of central tendency that can be used to best describe the average:

Continuous data - Mean
The mean is the most commonly used measure of central tendency and is best used for continuous data, such as heights or weights. To calculate the mean, you add up all of the data points and divide by the number of data points. For example, if you have the following data set: 2, 4, 6, 8, 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.

Ordinal data - Median
The median is the middle value in a data set and is best used for ordinal data, such as rankings or scores. To calculate the median, you first need to order the data set from smallest to largest. Then, if there are an odd number of data points, the median is the middle value. If there are an even number of data points, the median is the average of the two middle values. For example, if you have the following data set: 1, 2, 3, 4, 5, the median would be 3.

Nominal data - Mode
The mode is the most frequently occurring value in a data set and is best used for nominal data, such as categories or names. To calculate the mode, you simply count how many times each value appears in the data set and choose the one that appears most frequently. For example, if you have the following data set: A, A, B, B, B, C, C, the mode would be B.

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In a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

Linear Programming (LP) is an operation research approach used to determine the best outcomes, such as optimum profit, minimum cost, or maximum yield, given a set of constraints represented as linear relationships. Linear programming's fundamental idea is to find the best value of a linear objective function that takes into account a variety of constraints that are linear inequalities or equations. The goal of the constraints is to restrict the values of the decision variables. A linear programming problem consists of a linear objective function and linear inequality constraints, as well as decision variables. In a Linear Programming problem, we try to maximize or minimize a linear objective function, which represents our target. This objective function is expressed as a linear equation consisting of decision variables, each of which has a coefficient. Linear programming's ultimate goal is to find values of the decision variables that maximize or minimize the objective function while still satisfying the system of constraints we're working with. In this case, the objective function line is moved in the direction that reduces cost, which means we are minimizing the cost. We do this by moving the objective function line down towards the minimum point. This is the point where the objective function has the smallest possible value that meets all of the constraints.

Thus, in a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

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Answer:

103.5 m²

Step-by-step explanation:

To find the area of a right trapezoid, you can decompose it into a rectangle and a triangle. The sum of the area of  the rectangle and the triangle gives the area of the trapezoid.

For the right trapezoid attached below, the area can be gotten by:

Area of rectangle = length × breadth = 9 × 8 = 72 m²

Area of triangle = 1/2(base × height) = 0.5 × 7 × 9 = 31.5 m²

Area of trapezoid = Area of rectangle + Area of triangle = 72 m² + 31.5 m² = 103.5 m²